Robustness Analysis and Algorithm of Expected Shortfall Based on Extreme-Value Block Minimum Model

Abstract

To measure effectively the risk of stock market, the algorithm of expected shortfall is presented by using the extreme-value block minimum method. By transforming the distribution of standardized minimal return in an interval into the distribution of ordinary minimal return, the formula of expected shortfall is derived. By simulation and statistical analysis, an appropriate interval length is found out to make this algorithm robust. The simulation results show that the robustness of value at risk and expected shortfall based on this method is very good when the interval length isn’t more than 30. This algorithm measures effectively the expected shortfall of stock market.